If you're referencing it in Tanya, perek 36 is a very weak source, though it's somewhat implied there in connection with the yerida to create low olamos. You'd want to better refer to perek 31, where it says clearly that yeridah tzorech aliyah. My question is what is the source for the concept that EVERY yerida is tzorech aliyah, not just yeridas haneshomo lemato.

In Hisvaaduyos 5747, v. 2, p. 407, the Rebbe says: "This enabled him [the Frierdiker Rebbe] to spend the last ten years of his life disseminating Judaism, and striving to civilize the gentile world as well, as is known and famous, and has been printed." What is the Rebbe referring to, and where has it been printed?

The 1st two references have nothing to do with the principle of a yerida and aliyah ruchnis. The last one does, but it doesn't state there [Ben Porat Yossef, Vayechi, p. 85a (and see there also p. 85b), and Me’or Einayim, Va’etchanan, p. 62b-c.]--these sforim are not tachas yodi, so if anyone else can check the reference, I'd appreciate it] that this is a general principle. It only says it in connection with ha'alo'as machshovos zoros bifrat.

[As I understand it] Much older discussion and question than besht although terms might be new (and there are updated answers etc)... Will G-d willing provide page numbers when I return from my travels...

In footnotes, this is usually sourced to Ohr Hatorah from the Tzemach Tzedek. Though an earlier source would be where this is actually written in Likutei Torah. AFAIK, that's as far back as this idea goes.

What caught my eye when learning, is that the classic source for the concept as brought in marei m'koimos all throughout is: "Ohr Hatorah [D'vorim vol 2.] Eikev pg 481 and the citations brought there". With sources found in early Chassidus, why did all the editors seem to struggle over finding an actual "source" for this idea? As klal though, the T"T that I mentioned, has always become the "source" as penned down in seforim.

I thought that was pretty odd when I found the A"R to talk about this in Likutei Torah (as I mentioned in my first post). But now that the source shows to be in the BST's toiros as well, that only makes things even more odd...

These are just a few places I jotted down just in order to establish my point. But there are really many tens and tens of places that I didn't even mention - because it would just be too long to write out. So far, from what I've seen, they all bring this standalone citation...

In that maamor the T"T brings about 10 different maamorim in his citations on this idea, the earliest dating back to the A"R. It's interesting that the vort from the BST didn't get any mention in reference to this topic as addressed in sifrei Chassidus througought (as I've seen so far), neither from the T"T (or other Rebbeim in that case), or from the editors.